Q:
If two objects were drifting towards a black hole at the same speed and distance from the black hole, if they had different masses would the heavier one get "pulled" in first?

A:
This is a trick question. First, I assume you mean they are on radial
orbits. The newtonian answer is that the more massive object goes in
first (the black hole is attracted towards it more). Viewed from infinity, it
takes infinite time for an object to cross the event horizon. So,
technically, the General Relativity answer is that neither ever falls in. The Newtonian
answer will still be correct (to the extent that it makes sense) in the
General Relativity case, but off the top of my head I do not know what happens when they
get close to the event horizon. The effective horizon will be a little
larger for the more massive object, so I would be surprised if it does not
stay ahead of the lower mass object (in effect). Of course, if the two
are together (so they can influence one another) things can get very
messy (they could orbit one another). Even if they don't, the less
massive object would gain from the effect of the other object in moving
the black hole.